The statute of limitations for a wrongful death case is what would determine the filing deadline for this possible asbestos lawsuit, and that statute is state-specific. Across the country the range is one-year in a few states to two-years or three-years in most states. If you let me know the state of residence for your late husband at the time of his death I can be more precise.
As for the idea that there might be mesothelioma involved in your late husband's death, the autopsy may or may not be definitive. There are some pathology tests that can assist with making the diagnosis of mesothelioma, and it is possible that the autopsy process did not involve any of those tests. Even if it was lung cancer (as opposed to mesothelioma) that was involved with the death, you may still have a viable asbestos lawsuit depending on the several factors.
I suggest you have an asbestos-mesothelioma lawyer investigate this possible asbestos lawsuit for you. The attached resource, "Asbestos-Related Diseases and Legal Compensation", can help you get your bearings as regards this legal situation.
If you have any additional questions pertaining to this matter, feel free to contact me.
My best to you and your family in all aspects going forward.
I would just add that you need to also consider whether (and when!) your husband was diagnosed with any asbestos-related disease prior to his death, because the statute of limitations on the "pain and suffering" (i.e., personal injury) claim--which is typically distinct from the wrongful death claim--may run from the date your husband knew or should have known he had the relevant asbestos-related disease. Also, keep in mind that you may be able to sue in the state where your husband was exposed to asbestos, not just where he resided at the time of his death. If you wish to pursue a case, you should contact an asbestos attorney immediately.